Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
226 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10604068 | C2 | semidirect |
| 5. #10598646 | C2 | semidirect |
| 6. #170⋊C16 | C2 | semidirect |
| 7. #10598610 | C2 | semidirect |
| 108. #170 | SD32 | semidirect |
| 194. C5 | #12070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D8×#170 | 2 |
| #10604068 | 2 |
| #10599968 | 2 |
| #10598801 | 2 |
| #10598646 | 2 |
| #170⋊C16 | 2 |
| #10598610 | 2 |
| #12070 | 5 |